The dynamics of social agreement according to Conceptual Agreement Theory
Many social phenomena can be viewed as processes in which individuals in social groups develop agreement (e.g., public opinion, the spreading of rumor, the formation of social and linguistic conventions). Conceptual Agreement Theory (CAT) models social agreement as a simplified communicational event in which an Observer <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$(O)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mi>O</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> and Actor <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$(A)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> exchange ideas about a concept <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$C$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>C</mi> </math> </EquationSource> </InlineEquation>, and where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$O$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>O</mi> </math> </EquationSource> </InlineEquation> uses that information to infer whether <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$A$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>A</mi> </math> </EquationSource> </InlineEquation>’s conceptual state is the same as its own (i.e., to infer agreement). Agreement may be true (when <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$O$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>O</mi> </math> </EquationSource> </InlineEquation> infers that <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$$A$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>A</mi> </math> </EquationSource> </InlineEquation> is thinking <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$$C$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>C</mi> </math> </EquationSource> </InlineEquation> and this is in fact the case, event <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$$a1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>a</mi> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>) or illusory (when <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$$O$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>O</mi> </math> </EquationSource> </InlineEquation> infers that <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$$A$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>A</mi> </math> </EquationSource> </InlineEquation> is thinking <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$$C$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>C</mi> </math> </EquationSource> </InlineEquation> and this is not the case, event <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$$a2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>a</mi> <mn>2</mn> </mrow> </math> </EquationSource> </InlineEquation>). In CAT, concepts that afford <InlineEquation ID="IEq14"> <EquationSource Format="TEX">$$a1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>a</mi> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation> or <InlineEquation ID="IEq15"> <EquationSource Format="TEX">$$a2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>a</mi> <mn>2</mn> </mrow> </math> </EquationSource> </InlineEquation> become more salient in the minds of members of social groups. Results from an agent-based model (ABM) and probabilistic model that implement CAT show that, as our conceptual analyses suggested would be the case, the simulated social system selects concepts according to their usefulness to agents in promoting agreement among them (Experiment 1). Furthermore, the ABM exhibits more complex dynamics where similar minded agents cluster and are able to retain useful concepts even when a different group of agents discards them (Experiment 2). We discuss the relevance of CAT and the current findings for analyzing different social communication events, and suggest ways in which CAT could be put to empirical test. Copyright Springer Science+Business Media Dordrecht 2014